As the picture shows, when you are worried that the bottle in your hand will fall, you will always hold it tightly. What is the ultimate goal of doing this? (on physics)

Through force analysis, the bottle is subjected to gravity and friction in the vertical direction. These two forces are the balance forces when the bottle is at rest, and the friction force appearing in the static friction force is called static friction force. When the tangential external force increases gradually, but the two objects remain relatively static, the static friction increases with the increase of tangential external force, but the increase of static friction can only reach a certain maximum. When the tangential external force is greater than this maximum, two objects will move from relative rest to relative sliding. The maximum value of this static friction is called "maximum static friction".

When the static friction is not greater than the maximum static friction, the static friction and gravity are balanced, otherwise the bottle will slide down.